In this document, we will briefly introduce R and installing all the required packages for this course. A descriptive analysis of the dataset is then operated.
The following commands will load the package if they are already installed. If they are not yet installed, they will be installed and loaded afterwards. Note that for Windows users, Rtools is required for some packages (e.g., CASdatasets). This list may not be exhaustive and other packages may be required in other notebooks.
if (!require("xts")) install.packages("xts")
## Loading required package: xts
## Loading required package: zoo
##
## Attaching package: 'zoo'
## The following objects are masked from 'package:base':
##
## as.Date, as.Date.numeric
if (!require("sp")) install.packages("sp")
## Loading required package: sp
if (!require("CASdatasets")) install.packages("CASdatasets", repos = "http://cas.uqam.ca/pub/", type="source")
## Loading required package: CASdatasets
## Loading required package: survival
if (!require("caret")) install.packages("caret")
## Loading required package: caret
## Loading required package: ggplot2
## Loading required package: lattice
##
## Attaching package: 'caret'
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## cluster
if (!require("ggplot2")) install.packages("ggplot2")
if (!require("mgcv")) install.packages("mgcv")
## Loading required package: mgcv
## Loading required package: nlme
## This is mgcv 1.9-1. For overview type 'help("mgcv-package")'.
if (!require("dplyr")) install.packages("dplyr")
## Loading required package: dplyr
##
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## # #
## # The dplyr lag() function breaks how base R's lag() function is supposed to #
## # work, which breaks lag(my_xts). Calls to lag(my_xts) that you type or #
## # source() into this session won't work correctly. #
## # #
## # Use stats::lag() to make sure you're not using dplyr::lag(), or you can add #
## # conflictRules('dplyr', exclude = 'lag') to your .Rprofile to stop #
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if (!require("gridExtra")) install.packages("gridExtra")
## Loading required package: gridExtra
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## combine
if (!require("visreg")) install.packages("visreg")
## Loading required package: visreg
if (!require("MASS")) install.packages("MASS")
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if (!require("plotrix")) install.packages("plotrix")
## Loading required package: plotrix
if (!require("xtable")) install.packages("xtable")
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if (!require("scales")) install.packages("scales")
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if (!require("broom")) install.packages("broom")
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if (!require("stringi")) install.packages("stringi")
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if (!require("arrow")) install.packages("arrow")
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if (!require("patchwork")) install.packages("patchwork")
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if (!require("sf")) install.packages("sf")
## Loading required package: sf
## Linking to GEOS 3.12.1, GDAL 3.8.4, PROJ 9.3.1; sf_use_s2() is TRUE
if (!require("htmlwidgets")) install.packages("htmlwidgets")
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if (!require("leaflet")) install.packages("leaflet")
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require("CASdatasets")
require("ggplot2")
require("mgcv")
require("caret")
require("gridExtra")
require("dplyr")
require("visreg")
require("MASS")
require("plotrix")
require("xtable")
require("scales")
require("broom")
require("stringi")
require("arrow")
require("patchwork")
require("sf")
require("leaflet");
In this jupyter notebook, we will use the following options to set the width and height of our plots.
options(repr.plot.width = 8, repr.plot.height = 4, repr.plot.res = 250)
We will now load a dataset from the CASdatasets package. In case you were not able to install the CASdatasets package, we also provide a parquet file of the dataset (see more on that below).
We can simply load the dataset with the following command:
data("freMTPLfreq")
To keep it simple and illustrative, we will only keep a subset of this dataset. Each line corresponds to a policy. We will restrict ourselves to the policies covering a vehicle aged between 0 and 25 years. Also, we will only keep policies that were covered for a maximum of one year.
We will use the tidyverse universe in this course, as it can be easier to read (and writing clear code is important!). Subsetting can be done with the filter function.
dataset <- freMTPLfreq %>% filter(Exposure <= 1 & Exposure >= 0 & CarAge <= 25)
Note the pipe operator which allows to chain operations. We could also have written the following. We check that we obtain the same result with the all.equal(dataset, dataset_alternative) function. To save some memory we then remove the alternative dataset.
dataset_alternative <- freMTPLfreq %>%
filter(Exposure <= 1) %>%
filter(Exposure >= 0) %>%
filter(CarAge <= 25)
sprintf(
"Are the two datasets equal ? %s",
ifelse(all.equal(dataset, dataset_alternative), "Yes", "No")
)
## [1] "Are the two datasets equal ? Yes"
rm(dataset_alternative)
write_parquet(dataset, sink = "../data/dataset.parquet", compression = "gzip")
We will save the dataset into a parquet file, so we don’t need to load the CASdatasets package anymore and filter the data.
For those that could not install this package, now is the time to load the provided parquet file.
dataset <- read_parquet(file = "../data/dataset.parquet")
We can check that the dataset is correctly loaded with the following functions.A good idea is to check whether the dataset has been loaded correctly. To do this, the following tools can be used:
head(dataset)
## # A tibble: 6 × 10
## PolicyID ClaimNb Exposure Power CarAge DriverAge Brand Gas Region Density
## <fct> <int> <dbl> <fct> <int> <int> <fct> <fct> <fct> <int>
## 1 1 0 0.09 g 0 46 Japanes… Dies… Aquit… 76
## 2 2 0 0.84 g 0 46 Japanes… Dies… Aquit… 76
## 3 3 0 0.52 f 2 38 Japanes… Regu… Nord-… 3003
## 4 4 0 0.45 f 2 38 Japanes… Regu… Nord-… 3003
## 5 5 0 0.15 g 0 41 Japanes… Dies… Pays-… 60
## 6 6 0 0.75 g 0 41 Japanes… Dies… Pays-… 60
str(dataset)
## tibble [410,864 × 10] (S3: tbl_df/tbl/data.frame)
## $ PolicyID : Factor w/ 413169 levels "1","2","3","4",..: 1 2 3 4 5 6 7 8 9 10 ...
## $ ClaimNb : int [1:410864] 0 0 0 0 0 0 0 0 0 0 ...
## $ Exposure : num [1:410864] 0.09 0.84 0.52 0.45 0.15 0.75 0.81 0.05 0.76 0.34 ...
## $ Power : Factor w/ 12 levels "d","e","f","g",..: 4 4 3 3 4 4 1 1 1 6 ...
## $ CarAge : int [1:410864] 0 0 2 2 0 0 1 0 9 0 ...
## $ DriverAge: int [1:410864] 46 46 38 38 41 41 27 27 23 44 ...
## $ Brand : Factor w/ 7 levels "Fiat","Japanese (except Nissan) or Korean",..: 2 2 2 2 2 2 2 2 1 2 ...
## $ Gas : Factor w/ 2 levels "Diesel","Regular": 1 1 2 2 1 1 2 2 2 2 ...
## $ Region : Factor w/ 10 levels "Aquitaine","Basse-Normandie",..: 1 1 8 8 9 9 1 1 8 6 ...
## $ Density : int [1:410864] 76 76 3003 3003 60 60 695 695 7887 27000 ...
summary(dataset)
## PolicyID ClaimNb Exposure Power
## 1 : 1 Min. :0.00000 Min. :0.002732 f :95432
## 2 : 1 1st Qu.:0.00000 1st Qu.:0.200000 g :90663
## 3 : 1 Median :0.00000 Median :0.530000 e :76784
## 4 : 1 Mean :0.03925 Mean :0.559997 d :67660
## 5 : 1 3rd Qu.:0.00000 3rd Qu.:1.000000 h :26558
## 6 : 1 Max. :4.00000 Max. :1.000000 j :17978
## (Other):410858 (Other):35789
## CarAge DriverAge Brand
## Min. : 0.000 Min. :18.0 Fiat : 16653
## 1st Qu.: 3.000 1st Qu.:34.0 Japanese (except Nissan) or Korean: 79031
## Median : 7.000 Median :44.0 Mercedes, Chrysler or BMW : 19087
## Mean : 7.413 Mean :45.3 Opel, General Motors or Ford : 37287
## 3rd Qu.:12.000 3rd Qu.:54.0 other : 9738
## Max. :25.000 Max. :99.0 Renault, Nissan or Citroen :216684
## Volkswagen, Audi, Skoda or Seat : 32384
## Gas Region Density
## Diesel :205299 Centre :159426 Min. : 2
## Regular:205565 Ile-de-France : 69576 1st Qu.: 67
## Bretagne : 41986 Median : 288
## Pays-de-la-Loire : 38541 Mean : 1987
## Aquitaine : 31211 3rd Qu.: 1414
## Nord-Pas-de-Calais: 27111 Max. :27000
## (Other) : 43013
If one needs some help on a function, typing a question mark and the name of the function in the console opens the help file of the function. For instance,
?head
## starting httpd help server ... done
We will now proceed with a descriptive analysis of this dataset. We will now have a descriptive analysis of the portfolio. The different variables available are
names(dataset)
## [1] "PolicyID" "ClaimNb" "Exposure" "Power" "CarAge" "DriverAge"
## [7] "Brand" "Gas" "Region" "Density"
The variable PolicyID related to a unique identifier of the policy. We can check that every policy appears only once in the dataset
length(unique(dataset$PolicyID)) == nrow(dataset)
## [1] TRUE
Another possibility is to check the frequency of each PolicyID using the function table. The result is a table that shows for each PolicyID the corresponding number of lines in the dataset. We can then use a second time the function table in this result to show the frequency. We expect to have only ones (with possibily zeros), meaning each PolicyID has a unique line.
table(table(dataset$PolicyID))
##
## 0 1
## 2305 410864
To what corresponds the 0 ?
It appears that in this dataset the variable PolicyID is a factor. A factor variable has different levels. It appears that some PolicyID may be missing here (removed from the dataset, probably when we filtered out some policies). It is as if we had a 3-level categorical variable, for instance, color of a car, which takes three possible values: red, blue, gray, but in our dataset, we would only have red and blue cars. Gray would still be a level, but with no observation (i.e. no row) corresponding to a gray car.
To remove unused levels, we can use on the function droplevels.
dataset$PolicyID <- droplevels(dataset$PolicyID)
The Exposure reveals the fraction of the year during which the policyholder is in the portfolio. We can compute the total exposure by summing the policyholders’ exposures. Here we find:
sprintf("%s years", label_number(accuracy = 0.1)(sum(dataset$Exposure)))
## [1] "230 082.6 years"
We can show the number of months of exposure on a table. The function cut allows to categorize (bin) a numerical variable. We can specify where to ‘break’ and give a name to each level using the labels argument. The output is a factor variable.
table_exposures <- table(cut(dataset$Exposure,
breaks = seq(from = 0, to = 1, by = 1 / 12),
labels = 1:12
))
table_exposures
##
## 1 2 3 4 5 6 7 8 9 10 11
## 62633 29216 33452 24213 19463 29565 18835 14438 21518 13653 12422
## 12
## 131456
Using the function prop.table, it is possible to represent this information in relative terms show the number of months of exposure on a table.
exposures_prop <- prop.table(table_exposures)
round(exposures_prop, 4) * 100
##
## 1 2 3 4 5 6 7 8 9 10 11 12
## 15.24 7.11 8.14 5.89 4.74 7.20 4.58 3.51 5.24 3.32 3.02 32.00
Alternatively, we can use a barplot, using ggplot2 !
ggplot(dataset) +
geom_bar(
aes(x = cut(Exposure,
breaks = seq(from = 0, to = 1, by = 1 / 12),
labels = 1:12
))
) +
scale_x_discrete(name = "Number of months") +
scale_y_continuous(name = "Number of Policies", label = label_number()) +
ggtitle("Exposure in months")
What if we also want to show the percentage on the bars ?
ggplot(dataset, aes(
x = cut(Exposure, breaks = seq(from = 0, to = 1, by = 1 / 12), labels = 1:12),
label = scales::percent(prop.table(after_stat(count)), accuracy = 0.1)
)) +
geom_bar() +
geom_text(
stat = "count",
vjust = -0.5,
size = 3
) +
scale_x_discrete(name = "Number of months") +
scale_y_continuous(
name = "Number of Policies",
label = label_number()
) +
ggtitle("Exposure in months")
Note that a barplot is used to plot factor variables (categorical variables). In our case, we categorized the variable Exposure using the function cut. If we do not want to categorize this variable, we should use a histogram. We can specify the number of bins (= 12) or the binwidth (= 1/12).
ggplot(dataset, aes(x = Exposure)) +
geom_histogram(binwidth = 1 / 12, fill = "gray", color = "white") +
scale_x_continuous(
name = "Exposure in fraction of years",
breaks = seq(0, 1, 1 / 12),
labels = round(seq(0, 1, 1 / 12), 3)
) +
scale_y_continuous(name = "Number of Polices", labels = label_number()) +
ggtitle("Exposure in fraction of years")
If you are not familiar with ggplot, I could recommend this cheat-sheet: https://github.com/rstudio/cheatsheets/blob/main/data-visualization-2.1.pdf
ggplot(dataset, aes(x = ClaimNb)) +
geom_bar() +
geom_label(
stat = "count",
aes(label = percent(prop.table(after_stat(count)),
accuracy = 0.01
)),
vjust = 0.5
) +
scale_x_continuous(name = "Number of Claims") +
scale_y_continuous(
name = "Number of Polices",
labels = label_number()
) +
ggtitle("Proportion of policies by number of claims")
We can compute the average claim frequency in this portfolio, taking into account the different exposures.
label_percent(accuracy = 0.01)(sum(dataset$ClaimNb) / sum(dataset$Exposure))
## [1] "7.01%"
Let us now look at the other variables.
The variable Power is a categorized variable, related to the power of the car. The levels of the variable are ordered categorically. We can see the different levels of a factor by using the function level in R:
levels(dataset$Power)
## [1] "d" "e" "f" "g" "h" "i" "j" "k" "l" "m" "n" "o"
We can see the number of observations in each level of the variable, by using the function table.
table(dataset$Power)
##
## d e f g h i j k l m n o
## 67660 76784 95432 90663 26558 17398 17978 9270 4593 1758 1276 1494
Remember however, that in insurance, exposures may differ from one policyholder to another. Hence, the table above, does NOT measure the exposure in each level of the variable Power. We can use the functions group_by and summarise from package dplyr to give us the exposure in each level of the variable.
Check out the cheatsheet https://github.com/rstudio/cheatsheets/blob/main/data-transformation.pdf
power_summary <- dataset %>%
group_by(Power) %>%
summarise(
totalExposure = sum(Exposure),
Number.Observations = length(Exposure)
)
power_summary
## # A tibble: 12 × 3
## Power totalExposure Number.Observations
## <fct> <dbl> <int>
## 1 d 37571. 67660
## 2 e 44436. 76784
## 3 f 55652. 95432
## 4 g 51297. 90663
## 5 h 13800. 26558
## 6 i 9244. 17398
## 7 j 9228. 17978
## 8 k 4493. 9270
## 9 l 2134. 4593
## 10 m 919. 1758
## 11 n 642. 1276
## 12 o 666. 1494
We can show this on a plot as well:
plot_power_expo <- ggplot(power_summary, aes(
x = Power,
y = totalExposure,
fill = Power,
color = Power,
label = label_number()(totalExposure)
)) +
geom_bar(stat = "identity") +
geom_text(stat = "identity", vjust = -0.5) +
scale_y_continuous(
name = "Exposure in years",
labels = label_number(),
expand = expansion(mult = c(0, .15))
) +
scale_colour_discrete(guide = "none") +
scale_fill_discrete(guide = "none")
plot_power_expo
Let us now look at the observed claim frequency in each level
power_summary <- dataset %>%
group_by(Power) %>%
summarise(
totalExposure = sum(Exposure),
Number.Observations = length(Exposure),
Number.Claims = sum(ClaimNb),
Obs.Claim.Frequency = sum(ClaimNb) / sum(Exposure)
)
power_summary
## # A tibble: 12 × 5
## Power totalExposure Number.Observations Number.Claims Obs.Claim.Frequency
## <fct> <dbl> <int> <int> <dbl>
## 1 d 37571. 67660 2350 0.0625
## 2 e 44436. 76784 3198 0.0720
## 3 f 55652. 95432 3986 0.0716
## 4 g 51297. 90663 3450 0.0673
## 5 h 13800. 26558 998 0.0723
## 6 i 9244. 17398 715 0.0773
## 7 j 9228. 17978 710 0.0769
## 8 k 4493. 9270 375 0.0835
## 9 l 2134. 4593 162 0.0759
## 10 m 919. 1758 74 0.0805
## 11 n 642. 1276 55 0.0857
## 12 o 666. 1494 54 0.0811
We can compute the ratio to the portfolio claim frequency and plot the claim frequencies.
portfolio_cf <- sum(dataset$ClaimNb) / sum(dataset$Exposure)
# Can also be written as
portfolio_cf <- with(dataset, sum(ClaimNb) / sum(Exposure))
plot_power_claimfreq <- ggplot(power_summary, aes(
x = Power,
y = Obs.Claim.Frequency,
color = Obs.Claim.Frequency,
fill = Obs.Claim.Frequency,
label = percent(Obs.Claim.Frequency, accuracy = 0.01)
)) +
geom_bar(stat = "identity") +
geom_hline(aes(yintercept = portfolio_cf),
color = "black",
linewidth = 2,
linetype = "dashed",
alpha = 0.33
) +
geom_label(vjust = -0.21, fill = "white", alpha = 0.25) +
annotate(
geom = "text",
x = "m", y = portfolio_cf,
vjust = -0.5,
label = paste(
"Average claim freq. of portfolio: ",
percent(portfolio_cf, accuracy = 0.01)
),
color = "black"
) +
scale_y_continuous(
name = "Observed Claim Frequency", labels = label_percent(accuracy = 0.01),
expand = expansion(mult = c(0, .15))
) +
theme(legend.position = "none")
plot_power_claimfreq
With the package patchwork it is “ridiculously easy” (not my words :-) ) to combine separate ggplots. See below and see https://patchwork.data-imaginist.com/
plot_power_expo / plot_power_claimfreq
The vehicle age, in years. This is the first continuous variable that we encounter (although it only takes discrete values).
ggplot(
dataset,
aes(x = CarAge)
) +
geom_bar() +
scale_x_continuous(name = "Age of the Car", breaks = seq(0, 100, 5)) +
scale_y_continuous(name = "Number of Polices", labels = label_number())
Alternatively, we can use a histogram, with a binwidth of 1.
ggplot(
dataset,
aes(x = CarAge)
) +
geom_histogram(binwidth = 1, color = "black", fill = "white") +
scale_x_continuous(name = "Age of the Car", breaks = seq(0, 100, 5)) +
scale_y_continuous(name = "Number of Polices", labels = label_number())
Again, here, the exposures are not considered on the barplot/histogram. We can use ddply to correct this.
carage_summary <- dataset %>%
group_by(CarAge) %>%
summarise(
totalExposure = sum(Exposure),
Number.Observations = length(Exposure)
)
carage_summary
## # A tibble: 26 × 3
## CarAge totalExposure Number.Observations
## <int> <dbl> <int>
## 1 0 8711. 29984
## 2 1 18138. 37749
## 3 2 17347. 32505
## 4 3 15818. 28652
## 5 4 14966. 25761
## 6 5 14446. 23813
## 7 6 13790. 22433
## 8 7 12909. 20960
## 9 8 13084. 21091
## 10 9 12664. 20708
## # ℹ 16 more rows
Then, we can plot the data onto a barplot, as before.
ggplot(carage_summary, aes(
x = CarAge,
y = totalExposure,
fill = factor(CarAge),
color = factor(CarAge),
label = label_number(accuracy = 1)(totalExposure)
)) +
geom_bar(stat = "identity") +
geom_text(
stat = "identity",
color = "black",
hjust = 0.25,
vjust = 0.5,
angle = 45,
check_overlap = TRUE
) +
scale_x_continuous(breaks = seq(0, 100, 5)) +
scale_y_continuous(
name = "Exposure in years",
labels = label_number(),
expand = expansion(add = c(1000, 0), mult = c(0, .15))
) +
theme(legend.position = "none")
We can see a large difference, specially for new cars, which makes sense ! Indeed, let us look at the Exposure for recent vehicles, using a boxplot for instance.
ggplot(
dataset %>% filter(CarAge < 5),
aes(x = CarAge, y = Exposure, group = CarAge)
) +
geom_boxplot() +
ggtitle("Exposure of recent cars")
Let us now also compute the claim frequencies by age of car and plot them.
carage_summary <- dataset %>%
group_by(CarAge) %>%
summarise(
totalExposure = sum(Exposure),
Number.Observations = length(Exposure),
Number.Claims = sum(ClaimNb),
Obs.Claim.Freq = sum(ClaimNb) / sum(Exposure)
)
portfolio_cf <- with(dataset, sum(ClaimNb) / sum(Exposure))
ggplot(carage_summary, aes(
x = CarAge,
y = Obs.Claim.Freq,
label = percent(Obs.Claim.Freq, accuracy = 0.01)
)) +
geom_point() +
geom_line() +
geom_hline(
yintercept = portfolio_cf,
color = "black", linewidth = 2,
linetype = "dashed",
alpha = 0.33
) +
annotate(
geom = "text",
x = 20, y = portfolio_cf,
vjust = -0.5,
label = paste(
"Average claim freq. of portfolio: ",
percent(portfolio_cf, accuracy = 0.01)
),
color = "black"
) +
scale_x_continuous(name = "Age of the Car", breaks = seq(0, 100, 5)) +
scale_y_continuous(
name = "Observed Claim Frequency",
labels = label_percent(accuracy = 0.01)
) +
theme(legend.position = "none")
Similarly to the Age of the Car, we can visualize the Age of the Drivers.
driverage_summary <- dataset %>%
group_by(DriverAge) %>%
summarise(
totalExposure = sum(Exposure),
Number.Observations = length(Exposure),
Number.Claims = sum(ClaimNb),
Obs.Claim.Freq = sum(ClaimNb) / sum(Exposure)
)
head(driverage_summary, 9)
## # A tibble: 9 × 5
## DriverAge totalExposure Number.Observations Number.Claims Obs.Claim.Freq
## <int> <dbl> <int> <int> <dbl>
## 1 18 148. 497 46 0.310
## 2 19 637. 1610 171 0.268
## 3 20 1021. 2529 216 0.212
## 4 21 1278. 3040 207 0.162
## 5 22 1563. 3548 239 0.153
## 6 23 1830. 4156 230 0.126
## 7 24 2163. 4862 230 0.106
## 8 25 2496. 5556 240 0.0962
## 9 26 2937. 6468 312 0.106
We can show the Exposures by Age of the Driver…
ggplot(driverage_summary, aes(x = DriverAge, y = totalExposure)) +
geom_bar(stat = "identity", width = 0.8) +
scale_y_continuous(name = "Exposure in years", labels = label_number()) +
scale_x_continuous(name = "Age of the Driver", breaks = seq(10, 150, 10))
… and the observed claim frequency by Age.
ggplot(driverage_summary, aes(x = DriverAge, y = Obs.Claim.Freq)) +
geom_line() +
geom_point() +
scale_y_continuous(
name = "Observed Claim Frequency",
labels = percent,
breaks = seq(0, 0.50, 0.05)
) +
scale_x_continuous(name = "Age of the Driver", breaks = seq(10, 150, 10))
The variable Brand is a categorized variable, related to the brand of the car. We can see the different levels of a factor by using the function level in R:
levels(dataset$Brand)
## [1] "Fiat" "Japanese (except Nissan) or Korean"
## [3] "Mercedes, Chrysler or BMW" "Opel, General Motors or Ford"
## [5] "other" "Renault, Nissan or Citroen"
## [7] "Volkswagen, Audi, Skoda or Seat"
brand_summary <- dataset %>%
group_by(Brand) %>%
summarise(
totalExposure = sum(Exposure),
Number.Observations = length(Exposure),
Number.Claims = sum(ClaimNb),
Obs.Claim.Freq = sum(ClaimNb) / sum(Exposure)
)
brand_summary
## # A tibble: 7 × 5
## Brand totalExposure Number.Observations Number.Claims Obs.Claim.Freq
## <fct> <dbl> <int> <int> <dbl>
## 1 Fiat 9464. 16653 714 0.0754
## 2 Japanese (exce… 31229. 79031 2078 0.0665
## 3 Mercedes, Chry… 10392. 19087 828 0.0797
## 4 Opel, General … 21734. 37287 1731 0.0796
## 5 other 5676. 9738 412 0.0726
## 6 Renault, Nissa… 133460. 216684 8905 0.0667
## 7 Volkswagen, Au… 18127. 32384 1459 0.0805
ggplot(brand_summary, aes(
x = reorder(Brand, totalExposure),
y = totalExposure,
fill = Brand,
label = label_number()(totalExposure)
)) +
geom_bar(stat = "identity") +
coord_flip() +
guides(fill = "none") +
scale_x_discrete(name = "") +
scale_y_continuous("Exposure in years",
labels = label_number(),
expand = expansion(mult = c(0, 0.10))
) +
geom_label()
Let us now look at the claim frequency by Brand of the car.
ggplot(brand_summary, aes(
x = reorder(Brand, Obs.Claim.Freq),
y = Obs.Claim.Freq,
fill = Brand,
label = percent(Obs.Claim.Freq, accuracy = 0.1)
)) +
geom_bar(stat = "identity") +
geom_label(hjust = +1.2) +
coord_flip() +
guides(fill = "none") +
ggtitle("Observed Claim Frequencies by Brand of the car") +
scale_x_discrete(name = "Brand") +
scale_y_continuous(
"Observed claim Frequency",
labels = label_percent(accuracy = 0.1)
)
The variable Gas is a categorized variable, related to the fuel of the car. We can see the different levels of a factor by using the function level in R:
levels(dataset$Gas)
## [1] "Diesel" "Regular"
gas_summary <- dataset %>%
group_by(Gas) %>%
summarise(
totalExposure = sum(Exposure),
Number.Observations = length(Exposure),
Number.Claims = sum(ClaimNb),
Obs.Claim.Freq = sum(ClaimNb) / sum(Exposure)
)
ggplot(
gas_summary,
aes(
x = Gas,
y = totalExposure,
fill = Gas,
label = number(totalExposure)
)
) +
geom_bar(stat = "identity") +
geom_label() +
guides(fill = "none") +
scale_x_discrete(name = "Fuel") +
scale_y_continuous(
name = "Total Exposure (in years)",
labels = label_number()
)
There seems to be a similar amount of Diesel and Regular gas vehicles in the portfolio. It is generally expected that Diesel have a higher claim frequency. Does this also hold on our dataset ?
ggplot(
gas_summary,
aes(
x = Gas, y = Obs.Claim.Freq,
fill = Gas,
label = percent(Obs.Claim.Freq, accuracy=0.01)
)
) +
geom_bar(stat = "identity") +
geom_label() +
guides(fill = "none") +
scale_x_discrete(name = "Fuel") +
scale_y_continuous("Observed claim Frequency", labels = label_percent())
The variable Region is a categorized variable, related to the region of the place of residence. We can see the different levels of a factor by using the function level in R:
levels(dataset$Region)
## [1] "Aquitaine" "Basse-Normandie" "Bretagne"
## [4] "Centre" "Haute-Normandie" "Ile-de-France"
## [7] "Limousin" "Nord-Pas-de-Calais" "Pays-de-la-Loire"
## [10] "Poitou-Charentes"
What are the Exposures in each region ? What are the observed claim frequencies ?
region_summary <- dataset %>%
group_by(Region) %>%
summarize(
totalExposure = sum(Exposure),
Number.Observations = length(Exposure),
Number.Claims = sum(ClaimNb),
Obs.Claim.Freq = sum(ClaimNb) / sum(Exposure)
)
region_summary
## # A tibble: 10 × 5
## Region totalExposure Number.Observations Number.Claims Obs.Claim.Freq
## <fct> <dbl> <int> <int> <dbl>
## 1 Aquitaine 14223. 31211 1052 0.0740
## 2 Basse-Normand… 6622. 10848 451 0.0681
## 3 Bretagne 27657. 41986 1867 0.0675
## 4 Centre 101843. 159426 6460 0.0634
## 5 Haute-Normand… 3147. 8726 219 0.0696
## 6 Ile-de-France 30017. 69576 2575 0.0858
## 7 Limousin 2376. 4539 196 0.0825
## 8 Nord-Pas-de-C… 11347. 27111 939 0.0828
## 9 Pays-de-la-Lo… 21792. 38541 1569 0.0720
## 10 Poitou-Charen… 11059. 18900 799 0.0722
We can plot a map with the observed claim frequencies and the total Exposure. We first need to obtain the shape files (which contain the borders of each administrative area.)
# From http://www.diva-gis.org/gData
area <- sf::st_read(
"shapefiles/FRA_adm1.shp",
options = "ENCODING=UTF8"
)
## options: ENCODING=UTF8
## Reading layer `FRA_adm1' from data source
## `C:\Users\barigou\Dropbox\UCLouvain\Cours\LACTU2150 - Analyse statistique des données en assurance - GLM - GAM\UCLouvain-LACTU2150\1. Introduction\shapefiles\FRA_adm1.shp'
## using driver `ESRI Shapefile'
## Simple feature collection with 22 features and 9 fields
## Geometry type: MULTIPOLYGON
## Dimension: XY
## Bounding box: xmin: -5.143751 ymin: 41.33375 xmax: 9.560416 ymax: 51.0894
## Geodetic CRS: WGS 84
leaflet(area) %>%
addPolygons(
color = "#444444", weight = 1,
opacity = 1.0, fillOpacity = 0.5,
highlightOptions = highlightOptions(
color = "white", weight = 2,
bringToFront = TRUE
)
) %>%
addTiles()
We are now going to include our data into the map
area_w_data <- area %>% full_join(region_summary, by = c("NAME_1" = "Region"))
colors <- colorNumeric("YlOrRd", area_w_data$totalExposure)
# Create leaflet map
leaflet(area_w_data) %>%
addPolygons(
color = "#444444", weight = 1, smoothFactor = 0.5,
opacity = 1.0, fillOpacity = 0.5,
fillColor = ~ colors(totalExposure),
highlightOptions = highlightOptions(
color = "white", weight = 2,
bringToFront = TRUE,
),
popup = ~ paste(
"Region: ", NAME_1, "<br>",
"Exposure: ", round(totalExposure, 1)
)
) %>%
addTiles() %>%
leaflet::addLegend(
position = "bottomright",
pal = colors,
values = area_w_data$totalExposure,
title = "Total Exposure",
labFormat = labelFormat(suffix = ""),
opacity = 1
)